Let me fill you guys in on how all this works. I used to work for a company that refurbed phones for asurion and the wireless carriers. After that I worked for a wireless consulting firm and had contacts in Verizon's warehouse that filled me in on how it works.
If you buy a phone and return it because it is defective or broke they send it off to companies to be refurbed. At these companies it's all about production. You have a quota on how many phones you are supposed to refurb a day. It doesn't matter if the phone just needs the software re-flashed or if the screen needs to be replaced, your quota doesnt change. So if it's toward the end of the day and you are running behind you start to rush and some things dont get tested. Even if you're not rushing you only test it for a few min so if it's an intermittent problem you could very easily send the phone on as fixed if the problem didnt present itself in the 5 min you were testing it. These companies refurb phones for insurance companies as well as the carriers. They come in regular brown boxes, usually with no backs or batteries. These are used for warranty and insurance replacements.
If you purchase a phone but take it back for a non defective reason, like if you just didnt like it, Verizon repackages them and uses them as replacements. They normally arent tested, just cleaned up, factory reset and put back in the box. If the device is in perfect condition there is really no way to tell if it's been used or not. Verizon gives these out for warranty replacements.
Verizon will give out new devices if they don't have any refurbs or used devices in stock.
The CS reps have no way to tell which device you will get. The order is sent to the warehouse and the warehouse ships out what they have on hand at the time.